Gwibber - Gwibber is an open source microblogging client for GNOME developed with Python and GTK.
TweetDeck - TweetDeck is your personal browser for staying in touch with what’s happening now.
Choqok - Choqok - KDE Micro-Blogging Client The name comes from an ancient Persian word, means Sparrow!
Twitterfall - Twitterfall is an excellent choice if you want something basic, free and without much branding.
Tweetdeckr - Tweetdeckr is an open source Tweetdeck replacement client.
Earthquake - Terminal-based Twitter Client with Streaming API support. Only supports Ruby 1.9 and later.